Question

A small roller of diameter $20\text{cm}$ has an axle of diameter $10\text{cm}$ (see figure below on the left). It is on a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top of the axle (see figure on the right). The scale is now pushed slowly on the axle so that it moves without slipping on the axle, and the roller starts rolling without slipping. After the roller has moved $50\text{cm}$ , the position of the scale will look like :
(figures are schematic and not drawn to scale)

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

For no slipping at the ground ,

$V_{com}=\omega R$ ( $R$ is radius of roller)

$\therefore$ Velocity of scale = $V_{com}+\omega r$ [ r is radius of axle ]

$\therefore$Distance moved by scale = $(V_{com}+\omega r)t$

$=$$(V_{com}+\frac{V_{com}r}{R})t=\frac{3V_{com}}{2}.t$

$=75\text{cm}$

Therefore relative displacement (with respect to centre of roller) is $(75–50)\text{cm}$ = $25\text{cm}$